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Permuted & ordered power set

  1. Aug 17, 2008 #1
    I would like if there is a notion similar to that of a "power set" where the order of the elements in a set is accounted for - the elements are permuted, and each arrangement is considered to be a separate set.

    For example:

    For three singletons: {X},{Y}, & {Z} in a set S, the "ordered & permuted power set" would consist of the following subsets:

    {X}; {Y}; {Z};
    {X,Y}; {Y,X}; {X,Z}; {Z,X}; {Y,Z}; {Z,Y}
    {X,Y,Z}; {X,Z,Y}; {Y,X,Z}; {Z,X,Y}; {Y,Z,X}; {Z,Y,X}
  2. jcsd
  3. Aug 17, 2008 #2
    Please excuse my inexperience - I am new to set theory.
  4. Aug 23, 2008 #3
    Correction: In post #1, after the first three words, "I would like...", please add, "...to know...".
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